The spin-density-wave gap in (TMTSF)2ClO4

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Physica B 244 (1998) 121 124

The spin-density-wave gap in (TMTSF)2C104 V. V e s c o l i a'*, L. D e g i o r g i a, B. A l a v i b, G. G r i i n e r b " Laboratorium fiir Festkiirperphysik, Eidgeni~ssische Technische Hochschule, CH-8093 Ziirich, Switzerland b Department of Physics, Universi~ of California, Los Angeles, CA 90095-1547, USA

Abstract

We have measured the optical properties of the linear-chain compound (TMTSF)2C104 and AsF6, in the spindensity-wave state which develops below TsDw. In the direction perpendicular to the chains, we observe clear signatures of the spin-density-wave gap, similar to our previous findings in the (TMTSF)zPF 6 compound. ~-y 1998 Elsevier Science B.V. All rights reserved. Keywords: Far-infrared spectroscopy; Spin-density waves

The electrodynamics of the superconducting and the charge-density-wave states have been thoroughly explored and are well understood [1, 2]. In both cases, the response reflects the single particle and collective-mode excitations, with the so-called coherence factors playing an important role [1]. In the (s-wave, BCS) superconducting state, the zerofrequency mode is followed, for T = 0, by vanishing conductivity up to the gap frequency and then the absorption smoothly rises due to case II coherence effects [1]. The situation is somewhat different for the density-wave state in which case I coherence factors lead to a sharp maximum in the conductivity at the gap. The conductivity spectrum of a charge-density-wave system was first calculated by Lee et al. [3]. In contrast to these ground states, the electrodynamics of the spin-density-wave state (SDW) was little explored and understood [2, 4]. This is

* Corresponding author.

mainly for two reasons. First, experiments on linear-chain compounds, where the development of the SDW state leads to the full removal of the Fermi surface, have been performed along the highly conducting axis where the reflectivity is high (and consequently changes induced by the formation of the ground state are difficult to detect); and second, the normal-state properties are fundamentally different from those of a simple metal [5]. Recently, reflectivity measurements of (TMTSF)zPF 6 crystals gave indications for a SDW gap around 70 cm-1 perpendicular to the chains [6]. In order to further explore the gap issue in SDW systems we have conducted optical experiments on the Bechgaard salt (TMTSF)2AsF6 and C104 in a wide spectral range. The moderate conductivity perpendicular to the chain direction makes the exploration of the electrodynamics of the SDW state more accessible. As for the PF6 compound, we were able to directly detect and completely analyse the SDW gap. Particularly interesting is the C104 compound, which presents two possible broken-symmetry ground states depending on the cooling rate.

0921-4526/98/$19.00 (~2y 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 4 7 3 - 0

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Vescoli et al. /Physica B 244 (1998) 121 124

K

In fact, by slowly cooling through the anion-ordering phase transition at Ta = 24 K, one can reach a so-called unquenched state which will undergo a superconducting phase transition at T~ = 1.2 K I-4]. Otherwise, by fast cooling through T,, one reaches a so-called quenched state (corresponding to a freezing of the anions disorder), which will undergo a SDW phase transition at TsDw ~ 6 K [4]. By applying different cooling procedures, we can then single out the different ground states. We will present optical measurements in both the quenched and unquenched state of the C104 compound. All the experiments were performed on large single crystals. The wide crystals were slowly grown 102

10 l 100

........

i

103 ........

i

104 ........

i

during a period of six months by keeping the solution at low temperature (if>C) [6]. The optical reflectivity was measured in both polarizations parallel (E []a) and perpendicular (E Hb') to the chain direction using four different spectrometers which cover an extremely wide spectral range from 15 to 105cm -~ 1-5,6]. By performing the KramersKronig (KK) analysis one can then obtain the components of the optical conductivity. Figs. 1 and 2 display the optical reflectivity R(~o) of (TMTSF)zAsF6 and (TMTSF)2C104 measured in both polarizations, perpendicular and parallel to the chains, at temperatures above and below the SDW transition over a wide spectral range. Perpendicular to the chains (Fig. la and Fig. 2a) we find

[cm -1]

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................................................

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( T M T S F ) 2 C I O 4, Ellb \ \ ,,

--

\

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300 K

..... 200 K I O0 K •.............. 10 K

'1

20

__3oo ...... 4 0 K .............. 1 0 K

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I I I II;;;ll

: : '. ',I',l[ll

~:7.';~"

l I ~ :HIll

...........

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- . 2 ),

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(b)

~ . . - ~ : ~ . < 2 z Z ...........

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.... n,<.

g 60

60 '7-

},

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4o

( 20

-300 K ...... 200 K

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0

10-3

10-2

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100

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Photon Energy [eV] Fig. 1. The optical reflectivity R o f ( T M T S F ) 2 A s F 6 m e a s u r e d at various t e m p e r a t u r e s with polarization: (a) perpendicular; and (b) parallel to the c h a i n direction.

10-3

........

i

10-2

........

i

........

10-I

i

l00

.......

101

Photon Energy [eV] Fig. 2. The optical reflectivity R o f ( T M T S F ) 2 C I O 4 m e a s u r e d at various t e m p e r a t u r e s with p o l a r i z a t i o n (a) perpendicular; and (b} parallel to the chain direction.

E Vescoli et al. Physica B 244 (1998) 121 124

10o

*M*S'Fi'2 " ............ "O4,ENb

k~ ~10

-I

m e~

<

--10K - - 2.4 K, not quenched ........ 2.4 K, quenched 10-2 10-3

. . . . . . . .

i

. . . . . . . .

i

10-2 10-1 Photon Energy [eV]

. . . . . . . .

l0 0

Fig. 3. The low-frequency optical absorptivity (A = 1 - R) of (TMTSF)2CIO4 measured perpendicular to the chains (Ehlb') in the quenched and unquenched state. The S D W gap opens as the temperature is lowered below Tsvw in the quenched state only.

a well-developed plasma edge and a low-frequency behaviour, which above the transition can be qualitatively described, at least for the AsF 6 compound (Fig. 2a), as the response of a Drude metal. However, there remains a discrepancy between the optical and DC data which requires further investigation. For the C 1 0 4 compound, there seems to be a new broad feature in the FIR, overlapped to the low-frequency metallic component (Fig. 2a). This issue will be discussed in a forthcoming publication. Parallel to the chains (Fig. lb and Fig. 2b) the behaviour is somewhat more complicated and is discussed elsewhere [5]. What is important for this discussion of the electrodynamics of the SDW state is that optical measurements conducted parallel to the chains give no clear-cut evidence for the singleparticle gap nor for a SDW state. The situation is fundamentally different for the polarization direction perpendicular to the chains (EILb'). As clearly shown in Fig. la and Fig. 3, by decreasing the temperature below TsDw the reflectivity significantly decreases at frequencies below 50 70 cm 1, which is seen as evidence that a well-defined singleparticle gap develops. Note that for the C104 compound there is not any difference between R(co) at T > Tsuw and in the unquenched state (Fig. 3). Therefore, the FIR temperature dependence of

R(co) in

123

C104 is a typical feature of the quenched state. Coherence factors play an important role in the electrodynamics of the various broken symmetry ground states of metals. For the BCS superconducting state, case II coherence factors are associated with the transition induced by the electromagnetic wave. This leads to a smooth rise of the conductivity for frequencies co >/2A and to a reflectivity below the gap which is 100% at zero temperature. For density-wave states, case I coherence factors appear in the electrodynamic response, leading to a fundamentally different behaviour for frequencies around the single-particle gap [2]. In Ref. [5] the optical conductivity calculated for both case I and case II coherence factors was displayed. At zero temperature ~r1 is zero below the singleparticle gap, and we obtained a smooth rise of al(~O) for the superconducting case and a chacteristic square-root singularity at the gap frequency for the case of the SDW ground state. At finite temperatures, the contribution of the thermally excited electrons leads to a low-frequency tail, with progressively increasing spectral weight with increasing temperature [6]. From both components of the conductivity, the frequency-dependent reflectivity was calculated. For both the superconducting and the SDW case, sharp changes in reflectivity occur at the gap frequency. Well above the gap, the reflectivity is not sensitive to the development of the broken symmetry ground state. At zero temperature, the reflectivity below the gap is 100% for the superconducting case, while for the SDW ground state the reflectivity decreases and approaches a constant value as co --+ 0 [-6]. Spectral weight arguments play an important role for the superconducting state [1] and they are also important for the SDW ground state. As the collective mode is probably absent or insignificant in the direction perpendicular to the chains (and therefore does not contribute to the spectral weight), all the spectral weight of the Drude response found above TsDw is removed from the gap region and located in the single-particle response as the temperature is lowered below the transition. All the signatures calculated for case I coherence factors are observed by experiment (Fig. la and Fig. 3). Moreover, our results on the AsF6 and

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v. Vescoli et aL / Physica B 244 (1998) 121 124

C104 (quenched state) compounds agree with previous optical data on PF6 [-5, 6]. Thus, we conclude that the electrodynamics of the S D W ground state is qualitatively understood, for the case where the collective-mode contribution is negligible. The SDW-gap signature clearly affects the optical properties. For comparison, the infrared frequency dependence of the magneto-absorption of C104 grid is particularly relevant [4, 7]. An onset of magnetoabsorption below the energy gap, found as superconductivity, is destroyed by the magnetic field [7]. Nevertheless, for both compounds and similarly to PF6 [6] the magnitude of the gap 2A ~ 50-70 c m - ~ is significantly larger than what the weak coupling theory predicts. In this limit we expect, on the basis of the measured transition temperature T s o w , a value of 2A = 3.53 kBTsow (i.e., 2A ~ 15 or 3 0 c m -1 for C104, and AsF6 and PF6, respectively). Our larger gap values are also in contrast to the conclusion reached on the basis of DC resistivity measurements [4]. The reason for this, we believe, is that the D C resistivity is heavily influenced by a small number of states in the gap, leading to a serious underestimation of the magnitude of the gap. The large gap found here may be understood in terms of low-dimensional fluctuation effects [8]. These latter fluctuation effects are expected to be important below the mean-field transition temperature which we estimate as approximately TMF = 20 K. In summary, we have presented the optical properties of (TMTSF)zX with X = AsF6 and C104,

emphasizing particularly the SDW ground state with respect to the single-particle gap excitation. While parallel to the chains these organic systems are in the clean limit, for the perpendicular direction it is the dirty limit normal metallic state which provides the appropriate condition for the detection of the gap. The results turn out to bear a striking similarity with the P F 6 ones [-6]. Moreover, the absence of such a FIR excitation in the low-temperature unquenched state of C104 confirms the SDW gap nature of this absorption. We would like to thank J. Miiller for technical help during the measurements. This work was supported by the Swiss National Foundation for Scientific Research.

References [1] M. Tinkham, Introduction to Superconductivity, McGraw-Hill, New York, 1975. [23 G. Grfiner, Density Waves in Solids, Addison-Wesley, Reading, MA, 1994. [3] P.A. Lee, T.M. Rice, P.W. Anderson, Solid State Commun. 14-(1974) 703. [4] D. Jerome, H.J. Schulz, Adv. Phys. 31 (1982) 299. [5] M. Dressel, A. Schwartz, G. Griiner, L. Degiorgi, Phys. Rev. Lett. 77 (1996) 398. [63 L. Degiorgi, M. Dressel, A. Schwartz, B. Alavi, G. Grfiner, Phys. Rev. Lett. 76 (1996) 3838. [7] K. Ng, T. Timusk, J.M. Delrieu, D. Jerome, K. Bechgaard, J.M. Fabre, J. Phys. Lett. (Paris) 43 (1982) L513. [8] Fluctuation effectsof this kind have recently been found in charge-density-wavesystems;see B. Gorshunov et al., Phys. Rev. Lett. 73 (1994) 308.